Several organic cations derived from the same rigid bicyclic amine 1,3,3-trimethyl-6-azabicyclo[3.2.1]-octane have been used as structure-directing agents for the synthesis of pure silica zeolites in the presence of fluoride. The results are rationalized in terms of the varying size and rigidity of the cations. Both concepts were used in defining a large and rigid spiroammonium derivative which afforded the synthesis of the large pore pure silica zeolite ITQ-7. The existence of structural disorder in ITQ-7, which may be controlled through the water/silica ratio of the synthesis mixture, is confirmed by a number of techniques, but high-resolution electron microscopy results ruled out the existence of stacking faults. Thus, disorder in ITQ-7 does not appear to be due to intergrowths and may correspond to the existence of local defects, probably involving double four ring units, causing lattice strain mainly in the ab plane, according to X-ray diffraction simulations.